I would like to start developing a simple Workflow application in Sharepoint. What files should I download?
SharePoint Server 2007 SDK? SharePoint Server? SQL Server? Visual Studio? other?
Are they all required for workflow development?
I do not have SharePoint anywhere, please include its components in your answer.
If you don't have SharePoint installed, the free WSS 3.0 version is available for download from Microsoft. Follow these steps to install in a single server environment. It will install a basic version of SQL Server. Note this is suitable for prototyping only, not a production deployment, due to restrictions in the basic install.
Then use SharePoint Designer to create the workflows, free from Microsoft. There is no need for any other software. This allows you to configure workflow against a particular list in your SharePoint site with a wizard-like interface. See this topic on Office Online for more information.
If you need to develop a reusable workflow that can be deployed to many different sites or a production SharePoint instance then this is a much larger time investment. Start by reading one of the many other questions on this site for "getting started with SharePoint" that will give resources to how the product works. Be warned: there's a reasonable learning curve. Once you have a solid understanding, you could follow it up with a book such as Professional SharePoint 2007 Workflow Programming (first search result).
Another "warning" on designer...
The workflows you create there are allways fixed to a single list, and you cannot deploy them to a production server. So the "reusable" part from the above answer even includes a "portable" component.
Also those workflows are very static, since they only contain some speciffic actions that you can perform. (So no custom code etc).